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# Regression Analysis

This course will teach you how multiple linear regression models are derived, assumptions in the models, how to test whether data meets assumptions, and develop strategies for building and understanding useful models.

## Overview

Regression is perhaps the most widely used statistical technique. It estimates relationships between independent variables (predictors) and a dependent variable (outcome). Regression models can be used to help understand and explain relationships among variables; they can also be used to predict outcomes.

In this course you will learn fundamental concepts and be exposed to code examples (typically in R), learn to derive multiple linear regression models, how to use software to implement them, and what assumptions underlie the models. You will also learn how to test whether your data meets those assumptions, what can be done when those assumptions are not met, and strategies to build and understand useful models.

• Intermediate
• 4 Weeks
• Expert Instructor
• Tuiton-Back Guarantee
• 100% Online
• TA Support

## Learning Outcomes

After completing this course you should be able to calculate both simple and multiple regression models. You will learn how to assess the model’s “fit”, test model assumptions, and transform predictor and response variables to improve outcomes. You will also learn to identify critical aspects of the data that can influence results of your model and how to exercise caution with respect to extrapolation from regression results.

• Calculate a simple linear regression model
• Assess the model with standard error, R-squared, and slope
• Review and check model assumptions
• Extend the model to multiple linear regression
• Assess parameter estimates globally, in subsets, and individually
• Test model assumptions
• Deal with qualitative predictors
• Transform predictors and response variables to improve model fit
• Handle interactions among predictors
• Identify influential points
• Deal with autocorrelation, multicollinearity, and missing data
• Exercise appropriate caution with respect to extrapolation

## Who Should Take This Course

Scientists, business analysts, engineers and researchers who need to model relationships in data in which a single response variable depends on multiple predictor variables. If you were introduced to regression in an introductory statistics course and now find you need a more solid grounding in the subject, this course is for you. If you are planning to learn additional topics in statistics, a good knowledge of regression is often essential.

## Our Instructors

#### Dr. Iain Pardoe

Dr. Iain Pardoe teaches online and writes courses for Thompson Rivers University Open Learning.  He also does statistical consulting and was formerly an Associate Professor of Decision Sciences at the University of Oregon Lundquist College of Business. His research specialty is in the area of multivariate modeling. He has numerous journal publications (including a noted paper in the Journal of the Royal Statistical Society on predicting Academy Award winners).

## Course Syllabus

### Week 1

Foundations and Simple Linear Regression

• Brief review of univariate statistical ideas: confidence intervals
hypothesis testing
prediction
• confidence intervals
• hypothesis testing
• prediction
• Simple linear regression model and least squares estimation
• Model evaluation: regression standard error
R-squared
testing the slope
• regression standard error
• R-squared
• testing the slope
• Checking model assumptions
• Estimation and prediction

### Week 2

Multiple Linear Regression

• Multiple linear regression model and least squares estimation
• Model evaluation: regression standard error
R-squared
testing the regression parameters globally
testing the regression parameters in subsets
testing the regression parameters individually
• regression standard error
• R-squared
• testing the regression parameters globally
• testing the regression parameters in subsets
• testing the regression parameters individually
• Checking model assumptions
• Estimation and prediction

### Week 3

Model Building I

• Predictor transformations
• Response transformations
• Predictor interactions
• Qualitative predictors and the use of indicator variables

### Week 4

Model Building II

• Influential points (outliers and leverage)
• Autocorrelation
• Multicollinearity
• Excluding important predictors
• Overfitting
• Extrapolation
• Missing data
• Model building guidelines
• Model interpretation using graphics

## Class Dates

### 2024

01/12/2024 to 02/09/2024
Instructors: Dr. Iain Pardoe
05/03/2024 to 05/31/2024
Instructors: Dr. Iain Pardoe
10/11/2024 to 11/08/2024
Instructors: Dr. Iain Pardoe

### 2025

01/10/2025 to 02/07/2025
Instructors: Dr. Iain Pardoe
05/02/2025 to 05/30/2025
Instructors: Dr. Iain Pardoe
10/10/2025 to 11/07/2025
Instructors: Dr. Iain Pardoe

## Prerequisites

### Private: Statistics 1 – Probability and Study Design

This course, the first of a three-course sequence, provides an introduction to statistics for those with little or no prior exposure to basic probability and statistics.
• Skill: Intermediate
• Credit Options: ACE, CAP, CEU

### Private: Statistics 2 – Inference and Association

This course, the second of a three-course sequence, will teach you the use of inference and association through a series of practical applications, based on the resampling/simulation approach, and how to test hypotheses, compute confidence intervals regarding proportions or means, computer correlations, and use of simple linear regressions.
• Skill: Intermediate
• Credit Options: ACE, CAP, CEU

## Frequently Asked Questions

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## Register For This Course

Regression Analysis

## Additional Information

#### Time Requirements

About 15 hours per week, at times of your choosing.

#### Homework

Homework in this course consists of short answer questions to test concepts and guided data analysis problems using software.

#### Course Text

The required text for this course is Applied Regression Modeling, Third Edition by Iain Pardoe.

#### Software

You will need software that is capable of doing regression analysis, which all statistical software does.  If you are undecided about which package to choose, consider the following:

1.  If you are likely to take additional statistical modeling courses and intend to apply these methods to your research, you should choose a standard package with power and flexibility (R, SAS, JMP, SPSS, Minitab, Stata).

2.  If your plans include applications of data science and data analytics in business, you should probably choose R (if your company already uses SAS or SPSS, that’s also fine).

3.  If you want to work as a manager or analyst in business, but not as a data scientist, you could use an Excel add-in like XLStat or XLMiner (the latter does not cover all the procedures in the course).

4.  If you have no immediate plans for further coursework and a short learning curve is your main consideration, consider Statcrunch, JMP or Minitab.

The instructor is most familiar with R and Minitab. There will be some supplementary materials in the course to provide assistance with R, SPSS, Minitab, SAS, JMP, EViews, Stata, and Statistica. Our teaching assistants can offer some help with R, Minitab, SAS, JMP, Stata, Excel, and StatCrunch.

#### Literacy, Accessibility, and Dyslexia

At Statistics.com, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:

Chrome

Firefox

Safari

• Navidys (for colorblindness, dyslexia, and reading difficulties)
• HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)

## Register For This Course

Regression Analysis